On Dec 15, 2011, at 7:41 PM, <cbe...@tajo.ucsd.edu> wrote:
David Winsemius <dwinsem...@comcast.net> writes:
On Dec 15, 2011, at 11:34 AM, Mohamed Lajnef wrote:
Dear All,
Is there a method to diagnostic multicollinearty in logistic
regression
models like vif indicator in linear regression ( variance inflation
Factor ...) ?
Wouldn't matrix representation of the predictor "side" of the
regression be the same? Couldn't you just use the same methods you
employ for linear regression?
Harrell's rms package has a vif function that is intended for use with
fits from his logistic regression model function, lrm. This uses the
variance covariance matrix from the last iteration of the fitting
process alluded to below and Bert Gunter's reply.
Trouble is that in logistic regression the Fisher Information for each
case has a factor of p[i]*(1-p[i]) (where 'p' is the vector of success
probabilites and 'i' indexes which case).
If the value of p[i] is very near one or zero, then the information
provided is scant. And this will happen if you have a really good
predictor in the mix.
Even with an orthogonal design, you can wind up with huge variances.
And
you can have an ill-conditioned var-cov matrix for the coefficients
depending on how different cases get weighted. Thus, you could get the
equivalent of multicollinearity even with an orthogonal design.
And the diagnostics for linear regresson would not be all
that helpful if you have a good predictor.
OTOH, if the predictors were collectively pretty weak, the linear
regression diagnostics might be OK.
Mu advice: Google Scholar 'pregibon logistic regression', click
where it
says 'cited by ...' and page through the results to find good leads on
this topic.
Yes, that was an interesting exercise. Brought back many fond
memories. In my training we constructed df-betas and df-deviance
using GLIM macros. I think we may even have been given Pregibon's
paper, since he was a local boy (UW). When one learns logistic
regression on GLIM interacting with a VAX over a TTY line, R is a real
treat.
--
David Winsemius, MD
West Hartford, CT
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